Методические указания, контрольные работы по дисциплине "Математика" (2 семестр). Кузьмин С.Ю. - 20 стр.

                                                     Приложение 1.
              Таблица дифференцирования сложных функций

№    f (x)              f ′(x)     №      f (x)             f ′(x)
                                                         1
1     u   α       α u α −1 ⋅ u '   12     tgu                 ⋅ u'
                                                      cos2 u
                                                          1
2     au          a u ln a ⋅ u '   13    ctgu         − 2 ⋅ u'
                                                       sin u
                                                         1
3    eu              e u ⋅ u'      14   th u ⋅ u'         2
                                                             ⋅ u'
                                                       ch u
                        1                                 1
4    ln u                 ⋅ u'     15    cthu         − 2 ⋅ u'
                        u                               sh u
                                                         1
5    sin u          cos u ⋅ u'     16   arcsin u                ⋅ u'
                                                            2
                                                       1− u
                                                          1
6    cosu          − sin u ⋅ u'    17   arccos u    −             ⋅ u'
                                                              2
                                                        1− u

                                        arctg u       1
7    shu            ch u ⋅ u '     18
                                                         2
                                                           ⋅u'
                                                    1+ u

                                                           1
8    chu             sh u ⋅ u '    19   arcctg u    −         2
                                                                ⋅ u'
                                                         1+ u

9    c⋅ u               c ⋅ u'     20    u±v              u' ± v'

      u                 1
10                        ⋅ u'     21    u⋅v            u '⋅v + u ⋅ v '
      c                 с
      c                 c                  u            u'⋅v − u ⋅ v '
11                  −      ⋅ v'    22
      v                 v2                 v                 v2


                                   20